Answer
See the steps.
Work Step by Step
$LHS = 2 \sin^4{x} + 2 \sin^2{x} \cos^2{x} = 2\sin^2{x} (\sin^2{x}+\cos^2{x})$
$LHS = 2\sin^2{x} \times 1 =2\sin^2{x} = 1- \cos{2x} = RHS$
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